I was fortunate enough to see the solar eclipse in southern Illinois last year. The clouds were not friendly, but we did have one spectacular moment of perfect eclipse. It is an eerie sensation, and I cannot imagine how utterly terrifying it must have been for our ancient ancestors to see the moon eating the Sun.
However, it got me wondering. A solar eclipse can occur in the spectacular fashion it does because the angular dimension on the moon and the Sun are almost exactly the same -- this despite the fact that they are dramatically different in actual dimension. This seems a remarkable coincidence to me -- the ratio of the distances being almost exactly the same as the ratio of their diameters.
I was wondering if there are any other known examples of such a phenomenon occurring anywhere else in the universe? Can we make any estimate of how often something like that might occur in a galaxy?